LS-DYNA® Case Studies
Impact and Fracture Mechanics Assessment of a Fused Silica Window
Objective:
Determine the survival probability of a fused silica window subjected to a large particle impact event within a hypersonic wind tunnel using numerical methods (LS-DYNA) and fracture mechanics theories for brittle solids. If damage is predicted, provide an assessment of the windows’ service life under repetitive pressure cycling of 14 psi.
Modeling Assumptions and Details:
A finite element (FE) solid model of a 18” diameter, 1.5” thick disk was constructed based on information provided by the engineering team at Arnolds AFB (see Appendix). The FE model idealized a fused silica window that was potted into a steel frame using Ultracal 60 cement. The window is subjected to a differential pressure of 14 psi during hypersonic wind tunnel operation. This pressure tends to bow the window outward into the wind tunnel (internal side).
It is hypothesized that there exists a potential, during a specific wind tunnel test, for large particle debris (Pyroceram) to impact the window at high velocities (12.27 ft/s tangential and 10.18 ft/s normal to the window). A nominal particle size was determined (see Appendix) and idealized as a sphere with a diameter of 42.90 mm.
Mechanical property data for fused silica and Pyroceram 9606 is presented in the Appendix. It should also be noted that the mechanical properties for fused silica are similar at 25 and 176C. Data for Pyroceram 9606 at 176 C was not available but is believed to follow a similar trend as that for fused silica.
The analysis approach consists of model validation, impact simulation and interpretation of the results using fracture mechanics for brittle solids. Auxiliary static stress models are also used to provide additional substantiation of the fracture mechanics predictions. The FE model was built using Femap v10.02 and statically analyzed using NX Nastran v6.1. The transient dynamic impact analyses were performed using LS-DYNA v971 R4.2 for the Win64 platform.
Summary:
(i) Determine stress state in the fused silica window during and subsequent to the impact event using LS-DYNA. A LS-DYNA model was constructed of the impact event using two simulated particle sizes (42.90 mm (nominal size) and 12.7 mm). Stresses were calculated during and subsequent to the impact event. Impact stresses were found to be highly localized and the overall stress state of the window remains unchanged during and following impact. This result indicates that the particle can hit anywhere on the window and have approximately the same impact response (i.e., impact force on window and stress state within the window). Since fracture is dominantly initiated by tensile stresses, the following key results were determined: (a) the steady-state tensile stress in the window is ~4.0 MPa (580 psi); (b) the nominal particle created a peak tensile stress of ~17 MPa (2,466 psi) and the smaller particle created a peak tensile stress of ~6.3 MPa (910 psi).
(ii) Evaluate the window for its toughness or resistance to impact damage based on standard fracture mechanics principles.
Results from the LS-DYNA model show impact forces of 9,400 N (2,113 lbf) for the nominal particle size (42.90 mm diameter) and 1,060 N (238.3 lbf) for the smaller particle of 12.7 mm. Crack formation on the surface of the window is a function of impact force and sharpness of the contacting particle. A conservative approach was chosen for this analysis where the particle was assumed to be spherical and therefore presents a smooth contacting surface against the window. This allows a direct correlation with experimental fracture mechanics work conducted on fused silica where a spherical indenter having a diameter of12.7 mm was pressed against a fused silica plate. In this experimental work, small surface cracks were noted at loads greater than 600 N (134.9 lbf). Since the smaller spherical particle is shown to cause surface cracking on the window, fracture mechanics principles would then predict that for sharper particles the probability of surface cracking is even greater. Moreover, as the particles become larger (42.90 mm), the probability of crack formation would likewise scale. This allows one to conclusively state that if particles between the sizes of 12.7 to 42.90 mm impact the fused silica window at the stated velocities, surface cracking will appear on the window.
(iii) Provide an engineering assessment of the probability of the window surviving the impact event and if damaged, the largest flaw it could withstand and maintain its structural integrity A detailed FEA contact model of the sphere/window system was created to determine the contact stresses due to the particle debris impact.
The load for this model was the maximum contact force of 9,400 N (2,113 lbf). Stress results from this model were then used to drive the fracture mechanics calculations. In this work, it was argued that a crack of 5.7 mm (0.226”) deep would form during the impact event. Given a fused silica fracture toughness of 0.75 Mpa*m^0.5, calculations show that the window is able to withstand this flaw size and remain stable. That is, the catastrophic flaw size for the window under a differential pressure of 14 psi is 8.4 mm (0.331”). Therefore, the window should not fail during impact from Pyroceram debris.
The probability of window failure during the impact event is based on engineering judgment since no direct calculations exist. In this work, the worst possible particle configuration was assumed, that is, spherical. This assumption provides the absolute maximum impact force. From this analysis, the impact event was predicted to create a 5.74 mm deep crack. However, the propagation of this crack into the window for catastrophic failure is driven by the windows’ steady-state tensile stress field due to the differential pressure load and is decoupled from the impact event. Hence, if the particle hits away from the center of the window (i.e., outer radial impact), the impact induced crack will be more stable (lower tensile stress in the window) and less likely to cause failure of the window. Overall, given the conservative nature of this analysis and that the particle would have to hit near the center of the window, the probability of the window failing in a catastrophic manner is highly unlikely.
Long term stability of the window is difficult to predict since fused silica (glass) will tend to weaken due to moisture exposure. If the wind tunnel remains a dry environment then the impact induced crack should remain stable and not propagate during wind tunnel pressure cycling. It should be noted that the tolerable crack size is 8.4 mm (0.331”) and visual inspection should be able to detect a crack that is larger than 1/4 of an inch.
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